Hey. What's up, guys? So in this video, we're going to talk about calculating the angular momentum, l, of an object that has linear motion. Now remember, angular momentum is the momentum of an object that rotates. So it might seem weird to find the angular momentum of an object that is moving in a straight line that is not rotating. Let's check this out. It says here in some problems, an object moving in a straight line will collide against an object that is fixed in a rotating axis. So here, for example, I have these, sort of like a rotating door that's fixed about this axis. This object here will collide here and it will cause this door to spin this way, let's say. Right. So it is in a situation like this that the angular momentum of this guy, so the l of that object will make sense to be used.

Okay. So you may remember that we use linear momentum to solve collision problems. Well, to solve linear collision problems. So if you have a problem where both objects have linear velocity as they collide, then we're going to solve this, we're going to solve with linear momentum, with conservation of linear momentum. But if we have a situation where one object has a velocity v and another object has an omega like here, this object moves with a v. But then after the collision, the doors will have an omega. Then we're not going to use p to do this. We're going to use l. Okay. So I'm going to write here, we're going to solve this with l. Now if I have 2 objects with omega, so if you have 2 discs and they're both spinning and you push them against each other, that is an angular collision. I have an omega meeting up with another omega. And therefore, we're going to use not linear momentum but angular momentum.

These two here are probably obvious. If you have 2 linear motions, you use linear momentum. If you have 2, angular motions, you use angular momentum. What's interesting is the middle one, which is when you have one of each, l takes over. So what matters is the l, not the p. We're going to do some collision questions later, and you'll see this happen. So when we're trying to figure this out, in this case here, we need to first find the object's angular momentum, l, and not its linear momentum because of what I just said here. These questions will be solved with l. So I don't care what this guy's p is. I care what his l is. Okay? But the question is, how do we get the angular momentum? How do you get an angular momentum of an object that's moving in a straight line? This object isn't even rotating. How do I find its rotating momentum? Well, an object in a straight line has angular momentum relative to an unrelated axis of rotation. What do I mean? Is you can actually find the angular momentum of this guy relative to this axis even though they haven't really collided yet. Right? So it's an unrelated axis. So, hey, that axis over there, let's find an angular momentum relative to it. And we use the equation l=mvr. And notice, this is the same equation that we used for the angular momentum of a point mass.

Okay? So let's do an example and see what the deal is here. So, 2 rotating doors, each 6 meters long are fixed to the same central axis of rotation as shown above. This is a top view, which means you are looking down into the doors and you see them from the top. Okay. So we got those 2 there. And then suppose a bird, 4 kilogram bird, so the mass of this guy here, 4 kilograms. The bird moves with a velocity of 30. Horizontal, it's about to collide against the door at a point 50 centimeters from one end. Now it says here that it has 2 doors, which means we're talking about 1, 2, and the doors are 6 meters long. Okay. Which means each, each one of these points here is 3 meters long. So you can think of this as half a door. K. So it means that this whole thing here is 3 meters. Now the bird is colliding at 50 centimeters from one end. So the bird is colliding 50 centimeters from one end. Obviously, we're talking about this end and not this end. Okay. So this is 0.5 meters, which means that this distance here is 2.5 meters, 0.5-2.5. Okay. We want to know the bird's angular momentum about the axis to the center of the door just before hitting the door. So again, the angular momentum of an object in linear motion is given by l=m×v×r. Mass is 4, v is 30. Those are just plugged into the equation. And r is the distance from the axis of rotation to the point where it will touch. Okay. So just like a bunch of the other little r's that we've derived or that we've used, it's just a distance from the axis of rotation to the point where the point of interest, which is the point of collision. That distance is 2.5. Okay? So this is very straightforward. This is 0.5. So we're going to use this distance here because it collides here. So it's 2.5. So 2.5 goes right there. We multiply this whole thing and we have that this is 300 kilograms meters per meters squared per second. Okay. That's it. Just straightforward plug it in. Here, just warning you that this is going to come back later. It's going to make a return, when we fully solve these problems, these types of rotational collisions. So later on, this is going to collide. The door is going to spin and we're going to actually be able to calculate how fast the door spins. But not yet. So continue excitement and let's keep going. Let me know if you have any questions.